Optimal actuator placements for shape control of piezoelectric adaptive truss

With piezoelectric actuator as control element, this paper formulates the basic equations of shape control. A mathematical model of optimal actuator placements is presented. The actuator placements and the control voltages are taken as design variables, and the weighted presentation of the shape precision, control energy and number of actuators is taken as the objective function in this model. In addition, this model subjects to the strength of the structure, the limit of nodal displacement and the maximum control voltage of actuators. For the complex mixed variables optimization problem a new method is proposed, in which the approximate concepts, genetic algorithm and quadratic programming is combined. Firstly, the first level approximate problems are created through the multi-point approximate function, and then a layered optimization method is used, in the outside layer the actuator placement variables are optimized through the genetic algorithm, and in the inside layer the control voltage variables are optimized through the quadratic programming. The results of examples show that the proposed method has high efficiency.